Private sector investment and sponsorship for the iconic Library of Birmingham could fall £713,000 short of the projected target this year, leaving bosses looking for further savings.

The Library of Birmingham Development Trust, the facility’s charity fundraising arm, has reported that it may fall short of a its target of £1,075,000 this year.

The trust has committed to overcoming this shortfall through a £500,000 savings programme – although little is known about how this will be achieved – and raising a further £213,000 by next March, according to a report to the council’s cabinet.

The library already costs around £10 million a year to run, as well as £12 million a year repayments on loans to cover the £187 million construction costs.

A growing number of Birmingham’s ruling Labour group of councillors are asking serious questions about the ongoing costs of Europe’s largest public library at a time of major cuts in funding and services.

They are grumbling that while the library is something the city can be proud of – future generations are being saddled with a huge bill – and several took part in a protest over spiralling costs during the Conservative Party Conference two weeks ago.

But former Tory council leader Lord Mike Whitby, who drove the library project for five years, said that the finances were in order when he was replaced as leader in 2012.

Lord Whitby, a member of the library’s strategic board, said that he believed it reasonable, with the library’s global profile and reputation, that a significant level of private sponsorship could be delivered and blames the Labour council for stifling investment.

He said: “There is a large well of private social philanthropy and other countries are able to capture that. The cities that will thrive will be those who can also tap into that.

“I established the trust, as a charity, to run the library on the city’s behalf with the support of generous people – there would be freedom for the trust in how that funding would be used. That was the model and we had people lined up on that basis.

“But I believe that is no longer the model and that now the library and trust are being run as an extension of the council. It is very sad if philanthropy is being curtailed by a prescriptive relationship with the city council. The original concept has been watered down.”

A year since the library opened to the public, it has also emerged the building’s fuel and utility bills are £368,000 more than anticipated during construction and are placing a further pressure on the costs.

There is a one-off rate rebate of £278,000 which will mitigate the problem this year – the council will need to find the extra money or cut running costs in 2015/16.

Campaign group the Friends of the Libraries of Birmingham has accused the leadership of an “error of judgment” in setting such ambitious targets.

Spokesman Jolyon Jones said: “The budget saving was agreed without knowing the actual running costs of the new library or the fund raising potential of the trust. This figure was a ‘leap of faith’ when the council the budget in February and can now be seen as an error of judgement.

“We would be concerned that any shortfall in funds raised is likely to be met by direct cuts to library services.

“This saving figure is carried over for the next three years and is a potential black hole which threatens the future sustainability of the Library of Birmingham.”

He called on the council to fully review the funding situation and secure the future of the library.

Labour council deputy leader Ian Ward, responsible for the library, said that while the budget is a concern, “we are working through a robust budget process to identify solutions”.